<h2>Problem 216</h2>
<div style="color:#666;font-size:80%;">07 November 2008</div><br />
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<p>Consider numbers <var>t</var>(<var>n</var>) of the form <var>t</var>(<var>n</var>) = 2<var>n</var><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />-1 with <var>n</var> <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1.<br />
The first such numbers are 7, 17, 31, 49, 71, 97, 127 and 161.<br />
It turns out that only 49 = 7*7 and 161 = 7*23 are not prime.<br />
For <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 10000 there are 2202 numbers <var>t</var>(<var>n</var>)  that are prime.</p>

<p>How many numbers <var>t</var>(<var>n</var>) are prime for <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 50,000,000 ?</p>


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